Over 10 plays, a football team gained 63 yards. On 4 of the plays the team gained 0 yards, on 1 play the team lost 3 yards and on 1 play the team lost 6 yards. What was the team's mean gain, in yards, per play for the remaining plays?
4(0) + 1(-3) + 1(-6) + 4x = 63
Now just solve for x
To find the mean gain per play for the remaining plays, we need to subtract the yards gained on the non-remaining plays from the total gain and divide it by the number of remaining plays.
Let's calculate the total yards gained on non-remaining plays first.
- There were 4 plays in which the team gained 0 yards. This contributes 0 yards to the total gain.
- There was 1 play in which the team lost 3 yards. This contributes -3 yards to the total gain (negative because it's a loss).
- There was 1 play in which the team lost 6 yards. This contributes -6 yards to the total gain.
So, the total yards gained on non-remaining plays is 0 + (-3) + (-6) = -9 yards.
Now, let's calculate the total yards gained on the remaining plays. The total gain of 63 yards mentioned in the question already accounts for the non-remaining plays, so we just need to subtract the yards gained on those plays from the total gain:
Total gain - Yards gained on non-remaining plays = 63 - (-9) = 63 + 9 = 72 yards.
Finally, we divide the total yards gained on the remaining plays by the number of remaining plays to find the mean gain per play:
Mean gain = Total gain on remaining plays ÷ Number of remaining plays
Mean gain = 72 yards ÷ (10 - 4 - 1 - 1) plays
Mean gain = 72 yards ÷ 4 plays
Mean gain = 18 yards per play.
Therefore, the team's mean gain, in yards, per play for the remaining plays is 18 yards.